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I've some questions regarding svd:
Consider a matrix A ∈ R500×5 and its SVD [U, S, V T ] = svd(A).
(Assume A is centered).
a) is the second left singular vector of A is the direction in R5 with the second most variance?
b) is the first right singular vector of A is the direction in R5 with the most variance.
Let u1, u2 be the first two left singular vectors; let v1, v2 be the first two right singular vectors; and let s1, s2 be the first two singular values.
Consider $B = s1*u1*u^{T}_1+s2*u2*v^{T}_2$.
c) What is the dimension of B? d) What is the rank of B?